Answer:
You could fit 48 cubes with side lengths of 1/3 cm inside a rectangular prism with dimensions of 1 cm X 2 2/3 cm X 2/3 cm.
Step-by-step explanation:
The answer is -3 and 4. (-3)•4=-12 and -3+4=1
Answer:
Case 1:
![AB = 30](https://tex.z-dn.net/?f=AB%20%3D%2030)
![BC = 50](https://tex.z-dn.net/?f=BC%20%3D%2050)
Case 2:
![AB = 15.9](https://tex.z-dn.net/?f=AB%20%3D%2015.9)
![BC = 36.7](https://tex.z-dn.net/?f=BC%20%3D%2036.7)
Case 3: Not possible
Step-by-step explanation:
Given
See attachment for illustration of each case
Required
Find AB and BC
Case 1:
Using Pythagoras theorem in ANB, we have:
![AB^2 = AN^2 + BN^2](https://tex.z-dn.net/?f=AB%5E2%20%3D%20AN%5E2%20%2B%20BN%5E2)
This gives:
![AB^2 = 24^2 + 18^2](https://tex.z-dn.net/?f=AB%5E2%20%3D%2024%5E2%20%2B%2018%5E2)
![AB^2 = 576 + 324](https://tex.z-dn.net/?f=AB%5E2%20%3D%20576%20%2B%20324)
![AB^2 = 900](https://tex.z-dn.net/?f=AB%5E2%20%3D%20900)
Take square roots of both sides
![AB = \sqrt{900](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B900)
![AB = 30](https://tex.z-dn.net/?f=AB%20%3D%2030)
To calculate BC, we consider ANC, where:
![AC^2 = AN^2 + NC^2](https://tex.z-dn.net/?f=AC%5E2%20%3D%20AN%5E2%20%2B%20NC%5E2)
![40^2 = 24^2 + NC^2](https://tex.z-dn.net/?f=40%5E2%20%3D%2024%5E2%20%2B%20NC%5E2)
![1600 = 576 + NC^2](https://tex.z-dn.net/?f=1600%20%3D%20576%20%2B%20NC%5E2)
Collect like terms
![NC^2 = 1600 - 576](https://tex.z-dn.net/?f=NC%5E2%20%3D%201600%20-%20576)
![NC^2 = 1024](https://tex.z-dn.net/?f=NC%5E2%20%3D%201024)
Take square roots
![NC = \sqrt{1024](https://tex.z-dn.net/?f=NC%20%3D%20%5Csqrt%7B1024)
![NC = 32](https://tex.z-dn.net/?f=NC%20%3D%2032)
So:
![BC = NC + BN](https://tex.z-dn.net/?f=BC%20%3D%20NC%20%2B%20BN)
![BC = 32 + 18](https://tex.z-dn.net/?f=BC%20%3D%2032%20%2B%2018)
![BC = 50](https://tex.z-dn.net/?f=BC%20%3D%2050)
Case 2:
Using Pythagoras theorem in ANB, we have:
![AN^2 = AB^2 + BN^2](https://tex.z-dn.net/?f=AN%5E2%20%3D%20AB%5E2%20%2B%20BN%5E2)
This gives:
![24^2 = AB^2 + 18^2](https://tex.z-dn.net/?f=24%5E2%20%3D%20AB%5E2%20%2B%2018%5E2)
![576 = AB^2 + 324](https://tex.z-dn.net/?f=576%20%3D%20AB%5E2%20%2B%20324)
Collect like terms
![AB^2 = 576 - 324](https://tex.z-dn.net/?f=AB%5E2%20%3D%20576%20-%20324)
![AB^2 = 252](https://tex.z-dn.net/?f=AB%5E2%20%3D%20252)
Take square roots of both sides
![AB = \sqrt{252](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B252)
![AB = 15.9](https://tex.z-dn.net/?f=AB%20%3D%2015.9)
To calculate BC, we consider ABC, where:
![AC^2 = AB^2 + BC^2](https://tex.z-dn.net/?f=AC%5E2%20%3D%20AB%5E2%20%2B%20BC%5E2)
![40^2 = 252 + BC^2](https://tex.z-dn.net/?f=40%5E2%20%3D%20252%20%2B%20BC%5E2)
![1600 = 252 + BC^2](https://tex.z-dn.net/?f=1600%20%3D%20252%20%2B%20BC%5E2)
Collect like terms
![BC^2 = 1600 - 252](https://tex.z-dn.net/?f=BC%5E2%20%3D%201600%20-%20252)
![BC^2 = 1348](https://tex.z-dn.net/?f=BC%5E2%20%3D%201348)
Take square roots
![BC = \sqrt{1348](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B1348)
![BC = 36.7](https://tex.z-dn.net/?f=BC%20%3D%2036.7)
Case 3:
This is not possible because in ANC
The hypotenuse AN (24) is less than AC (40)
Answer:
Checked on edg. , the answer is A. Thanks!
Step-by-step explanation: